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A probabilistic relation between desirable and feasible, models of parallel computation

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Eli UpfalAuthors Info & Claims

STOC '84: Proceedings of the sixteenth annual ACM symposium on Theory of computing

Pages 258 - 265

https://doi.org/10.1145/800057.808689

Published: 01 December 1984 Publication History

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Abstract

We present a powerful probabilistic technique for simulating strong models of synchronized parallel computation by weaker ones. The technique is demonstrated by an algorithm simulating an n processor PRAM, with an arbitrary large shared memory, by an n processor ULRTACOMPUTER (a set of n processors communicating through a bounded degree network, and sharing no common memory). We prove that if a program required t PRAM steps, our simulation algorithm executes it on the ULTRACOMPUTER within O(tlog²n) steps with overwhelming probability.

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Bilardi GMoitra A(2005)Time lower bounds for CREW-PRAM computation of monotone functionsAutomata, Languages and Programming10.1007/BFb0035754(95-107)Online publication date: 29-Nov-2005
https://doi.org/10.1007/BFb0035754
Alt HHagerup TMehlhorn KPreparata F(2005)Deterministic simulation of idealized parallel computers on more realistic onesParallel Algorithms and Architectures10.1007/3-540-18099-0_24(11-15)Online publication date: 3-Jun-2005
https://doi.org/10.1007/3-540-18099-0_24
Rüdiger Reischuk K(2005)Parallel machines and their communication theoretical limitsSTACS 8610.1007/3-540-16078-7_90(359-368)Online publication date: 5-Jun-2005
https://doi.org/10.1007/3-540-16078-7_90
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Index Terms

A probabilistic relation between desirable and feasible, models of parallel computation
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic algorithms
    2. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods
      2. Sequential Monte Carlo methods
2. Theory of computation
  1. Models of computation
    1. Computability
      1. Turing machines

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STOC '84: Proceedings of the sixteenth annual ACM symposium on Theory of computing

December 1984

547 pages

ISBN:0897911334

DOI:10.1145/800057

Chairman:
Richard DeMillo

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 01 December 1984

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Bilardi GMoitra A(2005)Time lower bounds for CREW-PRAM computation of monotone functionsAutomata, Languages and Programming10.1007/BFb0035754(95-107)Online publication date: 29-Nov-2005
https://doi.org/10.1007/BFb0035754
Alt HHagerup TMehlhorn KPreparata F(2005)Deterministic simulation of idealized parallel computers on more realistic onesParallel Algorithms and Architectures10.1007/3-540-18099-0_24(11-15)Online publication date: 3-Jun-2005
https://doi.org/10.1007/3-540-18099-0_24
Rüdiger Reischuk K(2005)Parallel machines and their communication theoretical limitsSTACS 8610.1007/3-540-16078-7_90(359-368)Online publication date: 5-Jun-2005
https://doi.org/10.1007/3-540-16078-7_90
Spirakis P(2005)Input sensitive, optimal parallel randomized algorithms for addition and identificationSTACS 8610.1007/3-540-16078-7_66(73-86)Online publication date: 5-Jun-2005
https://doi.org/10.1007/3-540-16078-7_66
Herley K(1996)Representing shared data on distributed-memory parallel computersMathematical Systems Theory10.1007/BF0130531129:2(111-156)Online publication date: Apr-1996
https://doi.org/10.1007/BF01305311
Goldberg LMatias YRao SSnyder LLeiserson C(1994)An optical simulation of shared memoryProceedings of the sixth annual ACM symposium on Parallel algorithms and architectures10.1145/181014.181406(257-267)Online publication date: 1-Aug-1994
https://dl.acm.org/doi/10.1145/181014.181406
Harris T(1994)A survey of PRAM simulation techniquesACM Computing Surveys10.1145/176979.17698426:2(187-206)Online publication date: 1-Jun-1994
https://dl.acm.org/doi/10.1145/176979.176984
Herley KLeighton F(1990)Space-efficient representations of shared data for parallel computersProceedings of the second annual ACM symposium on Parallel algorithms and architectures10.1145/97444.97708(407-416)Online publication date: 1-May-1990
https://dl.acm.org/doi/10.1145/97444.97708
Luccio FPietracaprina APucci G(1990)A new scheme for the deterministic simulation of PRAMs in VLSIAlgorithmica10.1007/BF018404025:1-4(529-544)Online publication date: Jun-1990
https://doi.org/10.1007/BF01840402
Hornick SPreparata F(1989)Deterministic P-RAM simulation with constant redundancyProceedings of the first annual ACM symposium on Parallel algorithms and architectures10.1145/72935.72947(103-109)Online publication date: 1-Mar-1989
https://dl.acm.org/doi/10.1145/72935.72947
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Efficient in-place sorting algorithms using feasible parallel machine models

Some shared memory is desirable in parallel sparse matrix computation

Relations between concurrent-write models of parallel computation

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